View source for Liquid water potential temperature



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== liquid water potential temperature ==
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<div class="definition"><div class="short_definition">A quantity that is conserved in reversible [[adiabatic]] motion.</div><br/> <div class="paragraph">In the simplest approximation it is given by &#x003b8;<sub>''L''</sub>, where  <div class="display-formula"><blockquote>[[File:ams2001glos-Le23.gif|link=|center|ams2001glos-Le23]]</blockquote></div> with &#x003b8; the [[potential temperature]], ''L''<sub>''v''</sub> the [[latent heat]] of [[vaporization]], ''c''<sub>''pd''</sub> the [[specific heat]] of  [[dry air]] at constant [[pressure]], and ''r''<sub>''l''</sub> the [[liquid water mixing ratio]]. A more accurate expression  is  <div class="display-formula"><blockquote>[[File:ams2001glos-Le24.gif|link=|center|ams2001glos-Le24]]</blockquote></div> in which &#x003c7; is the [[Poisson constant]], &#x003b5; the ratio of the gas constants of dry air and [[water vapor]]  (0.622), ''r''<sub>''v''</sub> the mixing ratio of water vapor, ''c''<sub>''pv''</sub> the specific heat of water vapor, ''T'' the [[temperature]]  and &#x003b3; = ''r''<sub>''t''</sub>''R''<sub>''v''</sub>/(''c''<sub>''pd''</sub> + ''r''<sub>''t''</sub>''c''<sub>''pv''</sub>), where ''r''<sub>''t''</sub> is the [[total water mixing ratio]] and ''R''<sub>''v''</sub> the [[gas constant]] for  water vapor. Three quantities are conserved in reversible adiabatic motion: [[equivalent potential  temperature]], total water mixing ratio, and liquid water potential temperature. Any two of these  may be considered independent, with the third deducible from those two.</div><br/> </div><div class="reference">Deardorff, J., and K. A. Emanuel 1994. Atmospheric Convection. Oxford Univ. Press, . 580 pp. </div><br/> 
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